How can you model the spread of pollutants or the dynamics of ecosystems using Markov processes?

Feb 13, 2020 ... The current mathematical research in non-commutative probability and stochastic processes has been greatly influenced by scientific developments ... Oct 11, 2019 ... We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. The time-homogeneous Markov model asserts that one protein sequence is derived from another by a series of independent mutations, each changing one character in ... A continuous-time Markov process X can be conditioned to be in a given state at a fixed time T>0 using Doob's h-transform. This transform requires the ... We introduce and analyze a birth-death-suppression Markov process as a model of controlled culling of an abstract, dynamic population. In this paper we describe a general-purpose model of medical prognosis based on the Markov process and show how this simple mathematical tool may be used to ... This paper considers constrained Markov control processes in Borel spaces, with unbounded costs. The criterion to be minimized is a long-run expected average ... ... process of dimension 2. In this talk I will consider a path-valued Markov process defined by for. , where are the local times of . At first sight the ... Markov processes mathematically describe the mechanisms in the system, and predict the system's equilibrium behavior upon intervention, but do not support ... Other Markov models are based on the chain representations but with added information, such as observations and observation likelihoods. The transition matrix ...